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April 12th, 2014, 12:27 AM  #1 
Member Joined: Sep 2013 Posts: 84 Thanks: 2  Multiplicative inverse in factor ring?
Hello, can someone tell me how to find the multiplicative inverse of an element in a factor ring? Let the element be f and the factor ring T[x]/(m). The basic idea is to solve a diophantine equation like f*um*v=1,right?and we need to find u 
April 12th, 2014, 04:03 AM  #2 
Senior Member Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra 
You have the right idea â€“ except that an element of $T[x]/(m)$ is of the form $f+(m)$ where $f$ is a polynomial of degree at most $\deg(m)1$. When you have found a polynomial $u$ such that $fu=1+mv$ for some polynomial $v$, the multiplicative inverse of $f+(m)$ will be $u+(m)$.

April 12th, 2014, 04:05 AM  #3 
Member Joined: Sep 2013 Posts: 84 Thanks: 2 
i see,thanks


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